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9552b49 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | """Reproduce exact closure and the analytic rank-error frontier."""
import json
import sys
from pathlib import Path
import numpy as np
ROOT = Path(__file__).resolve().parents[1]
sys.path.insert(0, str(ROOT / "src"))
from oqaivaei.continuation import (
involution_pair, exact_closure, balanced_real_projector,
coordinate_minimax_error,
)
def run():
closures = []
for n in [3, 4, 5, 8, 12, 16]:
a, b, c = involution_pair(n)
combined = exact_closure([a, b], c)
closures.append({
"n": n, "rank_a": exact_closure([a], c).dimension,
"rank_b": exact_closure([b], c).dimension,
"rank_combined": combined.dimension,
"dimensions_by_round": combined.dimensions_by_round,
"maximum_retained_word_length": max(map(len, combined.words)),
})
rows = []
for n in [8, 16, 32, 64]:
for k in range(n + 1):
p = balanced_real_projector(n, k)
measured = coordinate_minimax_error(p)
expected = float(np.sqrt(1 - k / n))
rows.append({"n": n, "k": k, "formula": expected,
"constructed_error": measured,
"absolute_residual": abs(measured - expected)})
return {"exact_closures": closures, "rank_error_frontier": rows,
"max_absolute_residual": max(r["absolute_residual"] for r in rows),
"verification": "exact rational closure; floating-point projectors",
"data_kind": "synthetic mathematical instances"}
if __name__ == "__main__":
out = ROOT / "results" / "continuation_results.json"
out.parent.mkdir(exist_ok=True)
result = run()
out.write_text(json.dumps(result, indent=2) + "\n", encoding="utf-8")
print(json.dumps({"output": str(out), "exact_instances": len(result["exact_closures"]),
"frontier_points": len(result["rank_error_frontier"]),
"max_residual": result["max_absolute_residual"]}))
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